A wide neighbourhood primal-dual second-order corrector interior point algorithm for semidefinite optimization

Abstract

In this paper, we proposed a new primal-dual second-order corrector interior-point algorithm for semidefinite optimization. The algorithm is based on Darvay–Takács neighbourhood of the central path. In the new algorithm, the search directions are determined by the Darvay–Takács's direction and a second-order corrector direction in each iteration. The iteration complexity bound is for the Nesterov–Todd scaling direction, which coincides with the best-known complexity results for semidefinite optimization. Finally, numerical experiments show that the proposed algorithm is promising.